Move object continuously after being triggered by near sensor
Although you could have the reset distance at 10,000 blender units before it stops moving, and this may work for what you want, that is not at all the correct way to do this.

From what I can tell from your question, you want to have the cube detect being near the cylinder, and then after that, you want the cube to continuously move. The Near sensor detects the distance from the cylinder, and that sets the Boolean property to true. When the Boolean property is true, it will continuously make the cube move.

If you wanted to make the cube stop moving, you could simply have another property actuator assign the value of the property "PropName" to false. then the property "PropName" will obviously no longer be true, and thus "Property" (sensor) will no longer be true and will not send the positive pulses to "Motion" (actuator) and as a result, the motion will stop.